Fluid Mechanics

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Fluid Mechanics

Fluid Mechanics

Fluid mechanics is a branch of physics that studies the mechanics of fluids (liquids, gases, and plasmas) and the forces exerted on them. It is used in a wide range of disciplines, including mechanical, civil, chemical, and biomedical engineering, geophysics, oceanography, meteorology, astrophysics, and biology. can be divided into hydrostatics, which studies static fluids; and fluid dynamics, which studies the influence of force on fluid motion. It is a branch of continuum mechanics, a discipline that models matter without using information composed of atoms; that is, it simulates matter from a macroscopic perspective rather than a microscopic perspective.

Fluid mechanics, especially fluid dynamics, is an active and typical mathematically complex research field. Many problems are completely or partially unsolved, and it is best to use numerical methods to solve them, usually using a computer. A modern discipline called Computational Fluid Dynamics (CFD) is dedicated to this method. Particle imaging velocimetry is an experimental method used to visualize and analyze fluid flow. It also takes advantage of the high visibility of fluid flow.

Introductory Concepts and Definitions

Fluid Mechanics and Fluid Dynamics include a wide variety of subjects concerning the behavior of gases and liquids. In UE, we will mostly focus on the topic subset known as Aerodynamics, with a touch of Aerostatics thrown in for good measure.

Merriam Webster’s definitions:

Aerostatics: a branch of statics that deals with the equilibrium of gaseous fluids and solid bodies immersed in them

Aerodynamics: a branch of dynamics that deals with the motion of air and other gaseous fluids and with the forces acting on bodies in motion relative to such fluids

Hydrostatics and hydrodynamics are related to older concepts that are frequently employed in circumstances involving liquids. Surprisingly, there is a little basic distinction between the Aero– and Hydro– sciences. The main difference between them is in their applications (e.g. airplanes vs. ships).

Difference between a Solid and a Fluid (Liquid or Gas):

Solid: Applied tangential force/area (or shear stress) τ produces a proportional deformation angle (or strain) θ.

τ = Gθ

The constant of proportionality G is called the elastic modulus and has the units of force/area.

Fluid: Applied shear stress τ produces a proportional continuously-increasing deformation (or strain rate) θ

τ = µθ

The constant of proportionality µ is called the viscosity and has the units of force × time/area.


Properties of Fluids

Continuum vs molecular description of fluid

Molecules make up liquids and gases. Is the fluid’s distinct character essential to us? The answer in a liquid is NO. At macroscopic sizes, the molecules are in touch as they glide past one other and behave as a homogeneous fluid substance.

The molecules in a gas are not in direct touch. As a result, we must consider the mean free path, which is the average distance traveled by a molecule before colliding with another. Some air data that is known:

  • Mean free path at 0 km (sea level) : 0.0001 mm
  • Mean free path at 20 km (U2 flight) : 0.001 mm
  • Mean free path at 50 km (balloons) : 0.1 mm
  • Mean free path at 150 km (low orbit) : 1000 mm = 1m

The mean free path is far shorter than the average dimension of any atmospheric vehicle. Even though lift on a wing is caused by the impingement of discrete molecules, we may pretend the air is a continuum for the sake of determining lift. Calculating the small air drag on an orbiting spacecraft, on the other hand, necessitates considering the air as discrete isolated particles.

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